List the elements of a sample space for the simultaneous tossing of a coin and drawing of a card Class 9

List the elements of a sample space for the simultaneous tossing of a coin and drawing of a card Class 9

Question 1.

List the elements of a sample space for the simultaneous tossing of a coin and drawing of a card from a set of 6 cards numbered 1 through 6. Class 9

Solution:

Coin outcomes: {H, T}

Card outcomes: {1, 2, 3, 4, 5, 6}

∴ Sample space:

S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}

Question 2.

Three coins are tossed, and the number of heads is recorded. Which of the following lists is a sample space for this experiment? Why do the other lists fail to qualify as a sample space? Class 9

i. {1, 2, 3}

ii. {0, 1, 2}

iii. {0, 1, 2, 3, 4}

iv. {0, 1, 2, 3}

Solution:

When three coins are tossed, the possible number of heads can be:

0 head: TTT

1 head: HTT, THT, TTH

2 heads: HHT, HTH, THH

3 heads: HHH

∴ Sample space S = {0, 1, 2, 3}

{1, 2, 3} is missing 0 heads.

{0,1, 2} is missing 3 heads.

{0, 1, 2, 3, 4} includes 4 heads which is impossible with only 3 coins.

Hence they fail to qualify as sample space.