10 Shakir has to complete two tests. He can either pass or fail each test.
The probability that he will pass the first test is 0.87
If he passes the first test the probability he will pass the second test is 0.94 If he fails the first test the probability he will pass the second test is 0.73
(a) Complete the probability tree diagram for this information.(2)
(b) Work out the probability that Shakir passes at least one of the tests. (3)
Mark scheme (a)
Answer
Mark
Mark scheme
0.13, 0.94, 0.06, 0.73, 0.27
B2
for all values correctly placed
(B1
for at least 2 correct values placed)
Mark scheme (b)
Answer
Mark
Mark scheme
0.9649
M1
(ft their diagram) for one correct product, eg \(0.87 \times 0.94\ (= 0.8178)\) or \(0.87 \times 0.06\ (= 0.0522)\) or \(0.13 \times 0.73\ (= 0.0949)\) or \(0.13 \times 0.27\ (= 0.0351)\)
M1
for a full method, eg \(\text{``}0.8178\text{''} + \text{``}0.0522\text{''} + \text{``}0.0949\text{''}\) or \(1 - \text{``}0.0351\text{''}\)
A1
for 0.9649, 96.49% or \(\dfrac{9649}{10000}\)
Additional guidance
Allow values that are truncated or rounded as long as the intention is clear.
