Emergency flares are simple signalling devices similar to fireworks and they are designed to communicate a much more direct message in an emergency, for example, distress at sea. A company categorised their stocks of emergency flares as $1$-year old, $5$-year old and $10$-year old. The probabilities of successful firing of $1$-year old, $5$-year old and $10$-year old emergency flares are $0.995$, $0.970$ and $0.750$ respectively. Find the probability that, out of $100$ randomly chosen $1$-year old flares, at most $2$ fail to fire successfully. [1] One-year old flares are packed into boxes of $100$ flares. Find the probability that, out of $50$ randomly chosen boxes of $1$- year old flares, not more than $48$ of these boxes will have at most $2$ flares that will fail to fire successfully in each box. [3] Seven flares are chosen at random, of which one is $5$ years old and six are $10$ years old. Find the probability that the $5$-year old flare fails to fire successfully and at least $4$ of the $10$-year old flares fire successfully, [2] at least $4$ of the $7$ flares fire successfully. [3]

2019 NYJC P2 Q6

9 marks

Prelims

Emergency flares are simple signalling devices similar to fireworks and they are designed to communicate a much more direct message in an emergency, for example, distress at sea.

A company categorised their stocks of emergency flares as $1$-year old, $5$-year old and $10$-year old.

The probabilities of successful firing of $1$-year old, $5$-year old and $10$-year old emergency flares are $0.995$, $0.970$ and $0.750$ respectively.

Find the probability that, out of $100$ randomly chosen $1$-year old flares, at most $2$ fail to fire successfully.[1]
One-year old flares are packed into boxes of $100$ flares. Find the probability that, out of $50$ randomly chosen boxes of $1$- year old flares, not more than $48$ of these boxes will have at most $2$ flares that will fail to fire successfully in each box.[3]
Seven flares are chosen at random, of which one is $5$ years old and six are $10$ years old. Find the probability that
1. the $5$-year old flare fails to fire successfully and at least $4$ of the $10$-year old flares fire successfully,[2]
2. at least $4$ of the $7$ flares fire successfully.[3]

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