Advertisements
Advertisements
प्रश्न
Three groups of children contain respectively 3 girls and 1 boy, 2 girls and 2 boys and 1 girl and 3 boys. One child is selected at random from each group. What is the chance that three selected consists of 1 girl and 2 boys?
Advertisements
उत्तर
| Group-I | Group-II | Group-III | |||
| Girls | Boys | Girls | Boys | Girls | Boys |
| 3 | 1 | 2 | 2 | 1 | 3 |
Let G1, G2, G3 denote events for selecting a girl and B1, B2, B3 denote events for selecting a boy from 1st, 2nd and 3rd groups respectively.
Then P(G1) = `3/4`, P(G2) = `2/4`, P(G3) = `1/4`
P(B1) = `1/4`, P(B2) = `2/4`, P(B3) = `3/4`
Where G1, G2, G3, B1, B2, and B3 are mutually exclusive events.
Let E be the event that 1 girl and 2 boys are selected
∴ E = (G1 ∩ B2 ∩ B3) ∪ (B1 ∩ G2 ∩ B3) ∪ (B1 ∩ B2 ∩ G3)
∴ P(E) = P(G1 ∩ B2 ∩ B3) + P(B1 ∩ G2 ∩ B3) + P(B1 ∩ B2 ∩ G3)
= P(G1)·P(B2)·P(B3) + P(B1)·P(G2)· P(B3) + P(B1)· P(B2)·P(G3)
`=(3/4 xx 2/4 xx 3/4) + (1/4 xx 2/4 xx 3/4) + (1/4 xx 2/4 xx 1/4)`
= `(18 + 6 + 2)/64`
= `26/64`
= `13/32`
APPEARS IN
संबंधित प्रश्न
A card is drawn from a pack of 52 cards. What is the probability that card is either red or face card?
Hundred students appeared for two examinations. 60 passed the first, 50 passed the second, and 30 passed in both. Find the probability that student selected at random passed in exactly one examination.
Hundred students appeared for two examinations. 60 passed the first, 50 passed the second, and 30 passed in both. Find the probability that student selected at random failed in both the examinations.
If P(A) = `1/4`, `"P"("B") = 2/5` and `"P"("A" ∪ "B") = 1/2` Find the value of the following probability: P(A ∩ B)
If P(A) = `1/4`, P(B) = `2/5` and P(A ∪ B) = `1/2` Find the value of the following probability: P(A ∩ B')
If P(A) = `1/4`, P(B) = `2/5` and P(A ∪ B) = `1/2` Find the value of the following probability: P(A' ∩ B)
If P(A) = `1/4`, P(B) = `2/5` and P(A ∪ B) = `1/2` Find the value of the following probability: P(A' ∪ B')
If P(A) = `1/4`, P(B) = `2/5` and P(A ∪ B) = `1/2` Find the value of the following probability: P(A' ∩ B')
A card is drawn from a well shuffled pack of 52 cards. Find the probability of it being a heart or a queen.
In a group of students, there are 3 boys and 4 girls. Four students are to be selected at random from the group. Find the probability that either 3 boys and 1 girl or 3 girls and 1 boy are selected.
A, B, and C are mutually exclusive and exhaustive events associated with the random experiment. Find P(A), given that P(B) = `3/2` P(A) and P(C) = `1/2` P(B).
Two-third of the students in a class are boys and rest are girls. It is known that the probability of girl getting first class is 0.25 and that of boy getting is 0.28. Find the probability that a student chosen at random will get first class.
Two cards are drawn from a pack of 52 cards. What is the probability that, both the cards are either black or queens?
Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for which P(exactly one of A, B occurs) = `5/9`, is ______.
Four fair dice are thrown simultaneously. If the probability that the highest number obtained is 4 is `(25a)/1296` then 'a' is equal to ______.
