of 10 girls in a class, 3 speak French.If two girls are chosen at random, what is the probability that both speak french
3/10 * 2/9
To find the probability that both girls speak French, we need to first determine the total number of possible outcomes and the number of favorable outcomes.
Step 1: Total Number of Possible Outcomes
If we choose two girls at random, there are a total of 10 choose 2 ways in which we can pick a pair of girls. This can be calculated using the combination formula:
nCr = n! / (r! * (n-r)!)
Here, n represents the total number of girls (10 in this case), and r represents the number of girls we want to choose (2 in this case).
For our problem, 10 choose 2 can be calculated as follows:
10C2 = 10! / (2! * (10-2)!) = 45
So, there are 45 possible ways to choose two girls out of the 10.
Step 2: Number of Favorable Outcomes
We want to find the number of pairs of girls who both speak French. Since there are 3 girls who speak French, we can choose 2 out of them in 3 choose 2 ways.
3C2 = 3! / (2! * (3-2)!) = 3
So, there are 3 pairs of girls who both speak French.
Step 3: Calculate the Probability
The probability of an event is given by the ratio of the number of favorable outcomes to the number of total possible outcomes.
Probability = Number of favorable outcomes / Number of total possible outcomes
In this case, the probability of choosing two girls who both speak French is:
Probability = 3 / 45 = 1/15 = 0.0667 (rounded to four decimal places)
Therefore, the probability that both girls chosen at random speak French is approximately 0.0667 or 6.67%.