Question

You roll a 6-sided die with faces numbered 1 through 6, and toss a coin. What is the probability of rolling a 2 or getting heads? A.1/6

b. 5/12
c. 2/3
d. 1/12

Answer 1

The correct answer is option C, 2/3

Explanation:

Probability of an event = number of times the event occurred/total number of events

There are two set of events in this question –

Event A – Rolling a 6-sided die with faces numbered 1 through 6

In a die there are six faces numbered from 1 to 6

The probability of getting a six face = 1/6

Event B - Toss a coin.

There are two faces of a coin

The probability of getting either of the two faces = ½

When the two events A and B occur together , then the condition of A or B comes into picture. Thus the probability of either event A or event B

= Probability of event A + Probability of event B

= 1/6 + ½

= 4/6

= 2/3

Answer 2

in this instance a die is rolled and a coin is tossed. both events are independent of each other. the results of one event will not affect the results of the other event
event 1 - rolling a die
there are 6 sides with 1 side having 2
probability of getting 2 - 1/6
event 2 - tossing a coin
2 sides of which one is heads
probability of getting heads - 1/2

when we find the probability of rolling a 2 OR getting heads then we one of these events can happen or both the events can happen.
then we need to add the 2 probabilities of these 2 events happening

therefore probability of rolling a 2 or getting heads = 1/6 + 1/2
bring the fractions to a common denominator 6
1/2 multiply whole fraction by 3 --> 3/6
add the fractions

`(1)/(6) + (3)/(6) = (4)/(6)`
4/6 can be simplified by dividing whole fraction by 2

`(4/2)/(6/2) = (2)/(3)`
answer is 2/3