Problem Bank | IB Math AASL

[Maximum mark: 8]

Marisol takes one of two subway lines to work each morning, as illustrated in the tree diagram below.

Let:

Complete the following tree diagram.
$Marisol takes one of two subway lines to work each morning:<ul><li>She catches Line A with probability 25\tfrac{2}{5}52; otherwise she catches Line B (probability 35\tfrac{3}{5}53).</li><li>If she takes Line A, the probability she arrives on time is 34\tfrac{3}{4}43 (and hence is late with probability 14\tfrac{1}{4}41).</li><li>If she takes Line B, the probability she arrives on time is 13\tfrac{1}{3}31 (and hence is late with probability 23\tfrac{2}{3}32).</li></ul>Copy and complete the following tree diagram:<pre><code>pgsql</code></pre>CopyEdit$
[1]
Find the probability that Marisol catches Line A and is late.
[1]
Find the probability that Marisol is late on a given morning.
[2]
Given that Marisol is late, find the probability that she took Line A.
[2]
Over two consecutive workdays, find the probability that she is late at least once.
[2]

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[Maximum mark: 8]

Marisol takes one of two subway lines to work each morning, as illustrated in the tree diagram below.

Let:

Complete the following tree diagram.
$Marisol takes one of two subway lines to work each morning:<ul><li>She catches Line A with probability 25\tfrac{2}{5}52; otherwise she catches Line B (probability 35\tfrac{3}{5}53).</li><li>If she takes Line A, the probability she arrives on time is 34\tfrac{3}{4}43 (and hence is late with probability 14\tfrac{1}{4}41).</li><li>If she takes Line B, the probability she arrives on time is 13\tfrac{1}{3}31 (and hence is late with probability 23\tfrac{2}{3}32).</li></ul>Copy and complete the following tree diagram:<pre><code>pgsql</code></pre>CopyEdit$
[1]
Find the probability that Marisol catches Line A and is late.
[1]
Find the probability that Marisol is late on a given morning.
[2]
Given that Marisol is late, find the probability that she took Line A.
[2]
Over two consecutive workdays, find the probability that she is late at least once.
[2]

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Get hints, ask questions, and work through this problem step by step

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