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Alekssandra [29.7K]
3 years ago
12

A bag contains two coins, one for which the probability of heads is equal to 1 and one for which the probability of heads is equ

al to p. A coin is selected at random, and three independent tosses of this coin result in three heads. What is the probability that a further independent toss of this coin will produce a head?a. p4/1 + p3.b. p3 - p2/1 + p3.c. p3/1 - p.d. 1/1 + p3.e. 1 + p4/1 + p3.
Mathematics
1 answer:
wlad13 [49]3 years ago
5 0

Answer: Option E is the correct answer; (1 + p⁴) / (1 + p³)

Step-by-step explanation:

P (3 head) = P(first and 3 heads) + P(second coin and 3 heads)

= (1/2)×1³ + (1/2)× p³ = (1/2) × (1 + p³)

therefore P(first coin given 3 heads) = (1/2)×1³/ ((1/2)×(1 + p³))

= 1 / (1 + p³)

Also P( second coin given 3 heads) = p³ /(1 + p³)

therefore P(4th toss in heads given first 3 are heads)  will be;

= P(first and 4th toss heads) + P(second and 4th toss heads)

=(1/( 1 + p³ )) × 1 + p³ / (1+p³) × p

= (1 + p⁴) / (1 + p³)

Therefore Option E is the correct answer

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= 6.75 × 10^8

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How can you use a number line to order rational numbers? Give an example.
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If t varies 1/s and t=2 when s=60 find the relationship between t and s, b, find the value of t when s=90 c, find s when t=2,1/2
suter [353]

Answer:

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4 0
3 years ago
Ashley mixes two types of soft drinks with different types of concentration: one soft drink has 20% sugar and the other drink ha
ICE Princess25 [194]

Answer:

Sugar concentration of the mixed soft drink will be <em>32.5%.</em>

<em></em>

Step-by-step explanation:

Sugar concentration of first drink = 20%

Volume of first soda = 250 ml

Sugar in first soda = 20% of 250 ...... (1)

Sugar concentration of second drink = 45%

Volume of second soda = 250 ml

Sugar in second soda = 45% of 250 ...... (2)

Let x\% be the sugar concentration in resultant mixture.

Volume of mixture = 250 + 250 = 500 ml

Sugar in mixture = x\% of 500 ml ...... (3)

Total sugar concentration (Adding (1) and (2)) and equating it to equation (3):

20% of 250 + 45% of 250 = x\% of 500

\Rightarrow \dfrac{20}{100} \times 250 + \dfrac{45}{100} \times 250 =  \dfrac{x}{100} \times 500\\\Rightarrow 2 \times x = 65\\\Rightarrow x = 32.5\%

Hence, Sugar concentration of the mixed soft drink will be <em>32.5%.</em>

8 0
3 years ago
Write an equation of the line shown. Then use the equation to find the value of x when y=112
PtichkaEL [24]

Answer:

y = 8x + 16

x = 12

Step-by-step explanation:

Given two points on the line (0, 16) and (3, 40), an equation for the line can be written using the slope-intercept line equation which takes the format y = mx + b.

Where,

m = slope = \frac{y_2 - y_1}{x_2 - x_1}

b = y-intercept or the point at which the line cuts the y-axis.

Let's find slope (m) using the slope formula:

Let,

(0, 16) = (x_1, y_1)

(3, 40) = (x_2, y_2)

slope (m) = \frac{40 - 16}{3 - 0}

slope (m) = \frac{24}{3}

slope (m) = 8

Find b. Substitute the values of x = 0, y = 16, and m = 8 in the slope-intercept formula to find b.

y = mx + b

16 = 8(0) + b

16 = 0 + b

16 = b

b = 16

Plug in the values of m and b into the slope-intercept formula to get the equation of the line.

y = mx + b

y = 8x + 16

Let's use the equation to find x when y = 112.

y = 8x + 16

Substitute y = 112 in the equation

112 = 8x + 16

112 - 16 = 8x

96 = 8x

Divide both sides by 8

12 = x

x = 12

8 0
3 years ago
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