There are 10 black pearl and 5 white pearl in A box. There are 8black and 7white pearl in B box. More probability of black pearl from each of box is taken?
Answers
Given:
"A Box" has 10 black pearls and 5 white pearls.
"B Box" has 8 black pearls and 7 white pearls.
To find:
Which box (A or B) has a higher probability of getting a black pearl.
Solution:
"A Box" has 10 black pearls and 5 white pearls.
⇒ Total number of pearls in Box A = 10 + 5
⇒ Total number of pearls in Box A = 15 pearls.
"B Box" has 8 black pearls and 7 white pearls.
⇒ Total number of pearls in Box B = 8 + 7
⇒ Total number of pearls in Box B = 15
To know which box has a higher probability of getting a black pearl, we need to find the individual probabilities of getting a black pearl in both the boxes then compare them.
Probability of getting a black pearl in "Box A".
⇒ Probability(E) = (No: of Favourable outcomes)/(Total no: of outcomes)
Here, Let E = Probability of getting a black pearl in "Box A"
Favourable outcomes = 10
Total no: of outcomes = 15
⇒ Probability(E) = (No: of Favourable outcomes)/(Total no: of outcomes)
⇒ P(E) = 10/15
⇒ P(E) = 2/3
Probability of getting a black pearl in "Box B".
⇒ Probability(E) = (No: of Favourable outcomes)/(Total no: of outcomes)
Here, Let E = Probability of getting a black pearl in "Box B"
Favourable outcomes = 8
Total no: of outcomes = 15
⇒ Probability(E) = (No: of Favourable outcomes)/(Total no: of outcomes)
⇒ P(E) = 8/15
On comparing the probabilities on both boxes, we can say that the probability of getting a black pearl in "Box A" is higher.
(You can directly state that without any calculations as well since the total number of balls in both boxes are the same, i.e, 15)