Question

Each of 10 bins contain 1 piece of fruit. Two bins are oranges, 3 are apples, 4 are peaches, and 1 is a melon. What is the probability that you didn't choose two peaches

Answer 1

The probability of not choosing 2 peaches is $(\frac{13}{15} )$.

Step-by-step explanation:

Here, the total number of bins  = 10

Total orange bins  = 2

Total apples bins  = 3

Total peaches bins  = 4

Total melon bins  = 1

Let E : Event of picking two peaches

So, P(Picking 1 peach )  = $\frac{\textrm{Total peaches in bins}}{\textrm{Total bins}} = \frac{4}{10}$

and P (Picking 2nd  peach )  = $\frac{\textrm{Total peaches in bins}}{\textrm{Total bins}} = \frac{3}{9}$

$\implies P(E) = \frac{4}{10} \times\frac{3} {9} = \frac{2}{15}$

So, the probability of not picking 2 peaches  = 1 - P(picking  2 peaches)

$= 1 - (\frac{2}{15} ) = \frac{13}{15}$

Hence, the probability of not choosing 2 peaches is $(\frac{13}{15} )$.