Question

A fruit bowl contain 3 apples, 4 pears and 5 peaches. 4 fruits are randomly picked up from it. What is the probability that they are equal number of peaches and apples in the ones picked up ? Take in consideration the different ways that this fruits can be picked up.

Answer 1

We are given: 3 apples, 4 pears and 5 peaches then total sample = 3+4+5 = 12

P(apples) = 3/12 = 0.25

P(pear) = 4/12 = 0.33

P(peach) = 5/12 = 0.42

Here, 4 fruits are randomly picked.

Probability that they are equal number of peaches and apples.

Combinations: { (2 apples,2peaches), (1 apple, 1 peach, 2 pears), (0 apple, 0 peach, 4 pears) }

P(equal no. of apples and peaches) = P( 2 apple & 2 peaches) + P(1 apple & 1 peach & 2 pears) + P(4 pears)

= (3C2 * 5C2) / (12C4) + (3C1 * 5C1 * 4C2) / (12C4) + (4C4)/(12C4)

= (3*10)/495 + (3*5*6)/495 + (1/495)

= 121/495

= 0.2444

Probability that they are equal number of peaches and apples is 0.2444

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