Write the sample space and calculate the probability based on the given information. Class 9

Write the sample space and calculate the probability based on the given information. Class 9

Question 1.

Write the sample space and calculate the probability based on the given information. Class 9

i. Two coins are tossed at the same time. What is the probability of getting at least one head?

ii. Ten identical cards numbered 1 to 10 are placed in a box. One card is drawn at random. What is the probability of drawing a card with an even number?

iii. A die is rolled once. What is the probability of getting a number greater than 4?

iv. A bag contains 3 red balls, 2 blue balls, and 1 green ball. One ball is picked at random. What is the probability that it is not red?

v. Three coins are tossed simultaneously. What is the probability of getting exactly two heads?

Solution:

i. Sample space S = {HH, HT, TH, TT}

Total number of outcomes = 4

Favourable outcomes for at least one head E = {HH, HT, TH)

Number of favourable outcomes = 3

∴ P(at least one head)

$=\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}=\frac{3}{4}=0.75$

ii. Sample space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Total number of outcomes = 10

Favourable outcomes for even numbers E = {2, 4, 6, 8,10}

Number of favourable outcomes = 5

∴ P(even number) = $\begin{aligned} & =\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }} \\ & =\frac{5}{10}=\frac{1}{2}=0.5\end{aligned}$

iii. Sample space S = {1, 2, 3, 4, 5, 6}

Total number of outcomes = 6

Favourable outcomes for numbers greater than 4 : E = {5, 6}

Number of favourable outcomes = 2

∴ P(number greater than 4)

$=\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}=\frac{2}{6}=\frac{1}{3}=0.33$

iv. Total number of outcomes = total number of balls = 3 + 2 + 1 = 6

Not red means blue or green.

Number of favourable outcomes = Number of no red balls = 2 + 1 = 3

∴ P(not red) $\begin{aligned} & =\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }} \\ & =\frac{3}{6}=\frac{1}{2}=0.5\end{aligned}$

v. Sample space S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Total number of outcomes = 8

Favourable outcomes for exactly two heads: E = {HHT, HTH, THH}

Number of favourable outcomes = 3

∴ P(exactly two heads)

$=\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}=\frac{3}{8}$