Experimental probability = 1/5
Theoretical probability = 1/4
note: 1/5 = 0.2 and 1/4 = 0.25
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How I got those values:
We have 12 hearts out of 60 cards total in our simulation or experiment. So 12/60 = (12*1)/(12*5) = 1/5 is the experimental probability. In the simulation, 1 in 5 cards were a heart.
Theoretically it should be 1 in 4, or 1/4, since we have 13 hearts out of 52 total leading to 13/52 = (13*1)/(13*4) = 1/4. This makes sense because there are four suits and each suit is equally likely.
The experimental probability and theoretical probability values are not likely to line up perfectly. However they should be fairly close assuming that you're working with a fair standard deck. The more simulations you perform, the closer the experimental probability is likely to approach the theoretical one.
For example, let's say you flip a coin 20 times and get 8 heads. We see that 8/20 = 0.40 is close to 0.50 which is the theoretical probability of getting heads. If you flip that same coin 100 times and get 46 heads, then 46/100 = 0.46 is the experimental probability which is close to 0.50, and that probability is likely to get closer if you flipped it say 1000 times or 10000 times.
In short, the experimental probability is what you observe when you do the experiment (or simulation). So it's actually pulling the cards out and writing down your results. Contrast with a theoretical probability is where you guess beforehand what the result might be based on assumptions. One such assumption being each card is equally likely.
Answer:
1) 
2) 
3) 
4) 
Step-by-step explanation:
1) 
Solving using exponent rule: 
So,
2) 
Using the exponent rule: 
We have:
We also know that:
Using this rule:
So,
3) 
Solving:
So,
4) 
We know that:
So,
Answer: 
.
Step-by-step explanation: We are given expression .
And expression is converted in 
.
Now, we need to transform the expression into a single exponent expression using the properties of exponents.
We know, according to the properties of exponents
Applying same rule in given expression, we get
On simplifying exponents, we would get t in exponent.
= .
Distance of Sun and Mercury = 58,000,000 km.In Scientific notation, it would be: 5.8 × 10⁷ Km
Diameter of a human hair = 0.0025 cmIn scientific notation, it would be: 2.5 × 10⁻³ cm
Before Comparison, we need to bring cms to Kms or vice-versa, so we can easily calculate then, here, we will go from cm to Km.2.5 × 10⁻³ × 10⁻⁵ Km = 2.5 × 10⁻⁸
Now, we can compare the values, 5.8 × 10⁷ Km > 2.5 × 10⁻⁸
[ reason. - power of a smaller number is in negative, it means, it is denominator, which would be very small as compared to other ]
Hope this helps!
