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kakasveta [241]
3 years ago
6

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

juices.
Mathematics
1 answer:
lorasvet [3.4K]3 years ago
5 0

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

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