HSC Science (Computer Science) 11th Standard - Maharashtra State Board Question Bank Solutions

A, B, and C try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are `3/4, 1/2` and `5/8`. Find the probability that the target

1. is hit exactly by one of them
2. is not hit by any one of them
3. is hit
4. is exactly hit by two of them

The probability that a student X solves a problem in dynamics is `2/5` and the probability that student Y solves the same problem is `1/4`. What is the probability that

1. the problem is not solved
2. the problem is solved
3. the problem is solved exactly by one of them

Two hundred patients who had either Eye surgery or Throat surgery were asked whether they were satisfied or unsatisfied regarding the result of their surgery

The follwoing table summarizes their response:

If one person from the 200 patients is selected at random, determine the probability that the person was satisfied given that the person had Throat surgery.

Two hundred patients who had either Eye surgery or Throat surgery were asked whether they were satisfied or unsatisfied regarding the result of their surgery

The follwoing table summarizes their response:

If one person from the 200 patients is selected at random, determine the probability that person was unsatisfied given that the person had eye surgery

Two hundred patients who had either Eye surgery or Throat surgery were asked whether they were satisfied or unsatisfied regarding the result of their surgery.

The following table summarizes their response:

If one person from the 200 patients is selected at random, determine the probability the person had Throat surgery given that the person was unsatisfied.

Two dice are thrown together. Let A be the event 'getting 6 on the first die' and B be the event 'getting 2 on the second die'. Are the events A and B independent?

The probability that a man who is 45 years old will be alive till he becomes 70 is `5/12`. The probability that his wife who is 40 years old will be alive till she becomes 65 is `3/8`. What is the probability that, 25 years hence,

1. the couple will be alive
2. exactly one of them will be alive
3. none of them will be alive
4. at least one of them will be alive

A bag contains 3 yellow and 5 brown balls. Another bag contains 4 yellow and 6 brown balls. If one ball is drawn from each bag, what is the probability that, both the balls are of the same color?

A bag contains 3 yellow and 5 brown balls. Another bag contains 4 yellow and 6 brown balls. If one ball is drawn from each bag, what is the probability that, the balls are of different color?

Bag A contains 3 red and 2 white balls and bag B contains 2 red and 5 white balls. A bag is selected at random, a ball is drawn and put into the other bag, and then a ball is drawn from that bag. Find the probability that both the balls drawn are of same color

A bag contains 3 red and 5 white balls. Two balls are drawn at random one after the other without replacement. Find the probability that both the balls are white.

Solution: Let,

A : First ball drawn is white

B : second ball drawn in white.

P(A) = `square/square`

After drawing the first ball, without replacing it into the bag a second ball is drawn from the remaining `square` balls.

∴ P(B/A) = `square/square`

∴ P(Both balls are white) = P(A ∩ B)

`= "P"(square) * "P"(square)`

`= square * square`

= `square`

A family has two children. Find the probability that both the children are girls, given that atleast one of them is a girl.

Select the correct option from the given alternatives :

The odds against an event are 5:3 and the odds in favour of another independent event are 7:5. The probability that at least one of the two events will occur is

Solve the following:

If P(A ∩ B) = `1/2`, P(B ∩ C) = `1/3`, P(C ∩ A) = `1/6` then find P(A), P(B) and P(C), If A,B,C are independent events.

Solve the following:

If P(A) = `"P"("A"/"B") = 1/5, "P"("B"/"A") = 1/3` the find `"P"("A'"/"B")`

Solve the following:

If P(A) = `"P"("A"/"B") = 1/5, "P"("B"/"A") = 1/3` the find `"P"("B'"/"A'")`

Solve the following:

Let A and B be independent events with P(A) = `1/4`, and P(A ∪ B) = 2P(B) – P(A). Find P(B)

Solve the following:

Let A and B be independent events with P(A) = `1/4`, and P(A ∪ B) = 2P(B) – P(A). Find `"P"("A"/"B")`

Solve the following:

Let A and B be independent events with P(A) = `1/4`, and P(A ∪ B) = 2P(B) – P(A). Find `"P"("B'"/"A")`

Solve the following:

Find the probability that a year selected will have 53 Wednesdays