Data Handling — Statement I-II Type Questions

Statement I: Two coins are tossed simultaneously. The probability of getting different results on both the coins is $\dfrac{1}{2}$

Statement II: If E is an event, 0 ≤ P(E) ≤ 1

1. Statement I is true but Statement II is false.

2. Statement I is false but Statement II is true.

3. Both Statement I and Statement II are true.

4. Both Statement I and Statement II are false.

Answer

When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH and TT.

∴ Total number of outcomes = 4

The event is getting different results on both the coins and the outcomes HT, TH are favourable to the event.

So, the number of favourable outcomes = 2

⇒ P(getting different results) = $\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

= $\dfrac{2}{4}$

= $\dfrac{1}{2}$

So, Statement I is true.

The number of outcomes favourable to an event E is greater than or equal to 0 and is less than or equal to the total number of outcomes, so 0 ≤ P(E) ≤ 1.

So, Statement II is true.

∴ Both Statement I and Statement II are true.

Hence, option 3 is the correct option.

Statement I: A card is drawn randomly from a deck of cards. The probability of it being a card of honour is $\dfrac{4}{13}$

Statement II: P(E) = $\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes of the experiment}}$

1. Statement I is true but Statement II is false.

2. Statement I is false but Statement II is true.

3. Both Statement I and Statement II are true.

4. Both Statement I and Statement II are false.

Answer

By definition, P(E) = $\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes of the experiment}}$

So, Statement II is true.

There are 52 playing cards and one card is drawn.

∴ Total number of outcomes = 52

The event is getting a card of honour. The aces together with the face cards, that is 4 aces, 4 kings, 4 queens and 4 jacks, are called cards of honour.

∴ Number of cards of honour = 4 + 4 + 4 + 4 = 16

So, the number of favourable outcomes = 16

⇒ P(getting a card of honour) = $\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

= $\dfrac{16}{52}$

= $\dfrac{4}{13}$

So, Statement I is true.

∴ Both Statement I and Statement II are true.

Hence, option 3 is the correct option.