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There are 3 strawberry yoghurts, 2 peach yoghurts and 4 cherry yoghurts in a fridge.
Kate takes a yoghurt at random from the fridge.
She eats the yoghurt.
She then takes a second yoghurt at random from the fridge.
Work out the probability that both the yoghurts were the same flavour.

Respuesta :

lottearentsen08
There is a 3/9 = 1/3 chance that she takes 1 strawberry. So there is a 1/3*1/3 = 1/9 chance that she gets two.
Peach== 2/9*2/9 = 4/81 chance of two
And cherry == 4/9*4/9 = 16/81 of two.

So 1/9 + 4/81 + 16/81
= 9/81 + 4/81 + 16/81
= 29/81
= 0,358 chance
varshamittal029

The probability is 0.2778

The solution to the problem.

The probability of Kate taking the strawberry yogurt the first time is = 3/9

The probability of Kate taking a peach yogurt for the first time is = 2/9

The probability of Kate taking a cherry yogurt first time is = 4/9

Now for the second time, the total number of yogurts will change from 9 to 8 as any one of the yogurts has been consumed by kate so find the probability of kate eating yogurt will be subtracted by 1 if she had already consumed it once.

The probability of Kate taking the strawberry yogurt the second time is = 2/8

The probability of Kate taking a peach yogurt for the second time is = 1/8

The probability of Kate taking a cherry yogurt a second time is = 3/8

The probability that she consumes the same yogurt consecutively 2 times is = 3/9*2/8+2/9*1/8+4/9*3/8 = 20/72 = 5/18 = 0.2778

Hence the probability of the yogurt being of the same flavor is 0.2778

Learn more about probability here

https://brainly.com/question/6649771

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