Question

There are 10 cranberry and 15 strawberry juices. You randomly pick two juices. What's the probability you'll get two strawberry juices.

Answer 1

Answer:

• 7/20

Explanation:

The theoretical probability, P (A), of an event, A, is:

• P(A) = number of outcomes of event A / total number of possible outcomes

For 10 cranberry and 15 strawberry juices, the number of outcomes for two strawberry juices are:

• Combination of 15 strawberry juices chosen in two:

$C^{15}_{2}=\frac{15!}{(15-2)!(2!)}=\frac{15!}{13!2!}=\frac{15\times 14}{2}=105$

The total number of possible outcomes is:

• Combination of 25 juices chosen in two:

$C^{25}_{2}=\frac{25!}{(25-2)!(2!)}=\frac{25!}{23!2!}=\frac{25\times 24}{2}=300$

Thus, the probability of randomly picking two strawberry juices is:

• P (two strawberry juices) = 105/300 = 7/20

Note that you can obtain it as the product of the probabilities that the first juice is a strawberry juice and the second juice is also strawberry juice:

$15/25\times 14/24=(15\times 25)/(14\times 24)=210/600=7/20$