Final answer:
When tossing a fair coin four times, there are 9 different amounts of money that can be obtained: Rs. 4, Rs. 3, Rs. 1, Rs. 0, -Rs. 1.50, -Rs. 3, -Rs. 4.50, -Rs. 6. The probabilities of each amount can be calculated by dividing the number of outcomes with the same amount by the total number of outcomes.
Step-by-step explanation:
To calculate the number of different amounts of money and their probabilities, we need to analyze the possible outcomes of four coin tosses. Let's consider the sample space for this experiment:
- HHHH - Four heads
- HHHT - Three heads, one tail
- HHTH - Three heads, one tail
- HTHH - Three heads, one tail
- THHH - Three heads, one tail
- HHTT - Two heads, two tails
- HTHT - Two heads, two tails
- HTTH - Two heads, two tails
- TTHH - Two heads, two tails
- THHT - Two heads, two tails
- THTH - Two heads, two tails
- HTTT - One head, three tails
- TTHT - One head, three tails
- TTHT - One head, three tails
- TTTH - One head, three tails
- TTTT - Four tails
There are 16 possible outcomes in the sample space. Now, let's calculate the amount of money for each outcome:
- HHHH - Win Re 4
- HHHT - Win Re 3
- HHTH - Win Re 3
- HTHH - Win Re 3
- THHH - Win Re 3
- HHTT - Win Re 1
- HTHT - Win Re 1
- HTTH - Win Re 1
- TTHH - Win Re 1
- THHT - Win Re 1
- THTH - Win Re 1
- HTTT - Lose Rs. 1.50
- TTHT - Lose Rs. 1.50
- TTHT - Lose Rs. 1.50
- TTTH - Lose Rs. 1.50
- TTTT - Lose Rs. 6
There are 9 different amounts of money that can be obtained: Rs. 4, Rs. 3, Rs. 1, Rs. 0, -Rs. 1.50, -Rs. 3, -Rs. 4.50, -Rs. 6. The probabilities for each outcome can be calculated by dividing the number of outcomes with the same amount of money by the total number of outcomes. For example, the probability of winning Rs. 4 is 1/16, the probability of winning Rs. 1 is 5/16, and the probability of losing Rs. 6 is 1/16.