EasyMathematicsHigh School (11–12)Statistics and Probability › Random Variables and Probability DistributionsNumericalAP A-Level IB

A netball player scores from a free shot with probability 0.7, independently each time…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A netball player scores from a free shot with probability $0.7$ , independently each time. She takes $6$ shots. Find the probability that she scores exactly $4$ times. Find the probability that she scores every time. Find the mean number of goals. Give the probabilities to four decimal places.

Need a reminder? The key ideaShow

For $n$ independent trials with success probability $p$ and $q = 1 - p$ , $P(X = k) = \binom{n}{k}p^k q^{n-k}$ , with mean $np$ and variance $npq$ . Check the four conditions first: fixed $n$ , two outcomes, the same $p$ , independent trials.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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