Question
Suleika has six cards numbered 1 to 6.
(a) She takes one card at random, records the number and replaces the card.
(i) Write down the probability that the number is 5 or 6.
………………………………………….
(ii) Suleika does this 300 times.
Find how many times she expects the number 5 or 6.
………………………………………….
(b) Suleika takes two cards at random, without replacement.
(i) Find the probability that the sum of the numbers on the two cards is 5.
………………………………………….
(ii) Find the probability that at least one of the numbers on the cards is a square number.
………………………………………….
Answer/Explanation
(a)(i)\(\frac{1}{3}\)
(ii)100
(b)(i)\(\frac{2}{15}\)
(ii)\(\frac{3}{5}\)
Question
(a) A shop gives each of 1000 people a voucher.
28 people use their voucher.
The shop now gives each of 16500 people a voucher.
Calculate how many of these 16500 people are expected to use their voucher.
………………………………………….
(b) In a class activity, all the 15 students wear hats.
7 students wear red hats, 6 students wear green hats and 2 students wear white hats.
(i) One of these students is picked at random.
Find the probability that this student wears a red hat.
………………………………………….
(ii) Two of the 15 students are picked at random.
Show that the probability that these two students wear hats of the same colour is \(\frac{37}{105}\)
(iii) Three of the 15 students are picked at random.
Find the probability that at least two of these three students wear red hats.
………………………………………….
Answer/Explanation
(a) 462
(b)(i)\(\frac{7}{15}\)
(ii)\(\frac{7}{15}\times \frac{6}{14}+\frac{6}{15}\times \frac{5}{14}+\frac{2}{15}\times \frac{1}{14}\)
\(=\frac{37}{105}\)
(iii)\(\frac{29}{65}\)
Question
Ravi spins a biased 5-sided spinner, numbered 1 to 5.
The probability of each number is shown in the table.
(a) Find the value of x.
x = …………….
(b) Ravi spins the spinner once.
Find the probability that the number is 2 or 3.
(c) Ravi spins the spinner twice.
Find the probability that
(i) the number is 2 both times,
(ii) the sum of the numbers is 3.
(d) Ravi spins the spinner 72 times.
Calculate how many times he expects the number 1.
Answer/Explanation
Answer:
(a) \(\frac{1}{8}\) oe
(b) \(\frac{7}{12}\) oe
(c) (i) \(\frac{1}{16}\) oe
(ii) \(\frac{2}{24}\) oe
(d) 12